I did a similar thing for a flap indicator for an aircraft which used a non-linear rehostat as a position indicator, but I didn't use an LM3914. I made my own LM3914 equivalent out of 8 LM339 comparators. This gave me the opportunity to make the steps monotonic, but non-equal.
I recorded the voltage out of the sender at steps of 5deg out of a total travel of 40deg. I created a voltage divider with 9 resistors (8 taps) where the voltages at the taps correspond to the 5deg steps. Note the B-source at the bottom of this simulation. Note the coefficients in the polynomial that describes the voltage of this source vs time. Note that in the simulation, 1 degree of flap travel = 1 sec.
You could do the same by filling your tank 1 gal at a time, and recording the voltage across the sender at each point. Put the points into EXCEL, and use the least-squares curve fit function to find the coefficients of a quadratic or higher order polynomial function through your points. You can then evaluate that polynomial at eight equal steps, and that will lead to a similar non-equal step voltage divider...